New Observations on Complex RTN in Scaled High-κ/Metal-gate MOSFETs – the Role of Defect Coupling under DC/AC Condition

Pengpeng Ren1, Peng Hao1, Changze Liu1, Runsheng Wang1*, Xiaobo Jiang1, Yingxin Qiu1, Ru Huang1*, Shaofeng Guo1, Mulong Luo1, Jibin Zou1, Meng Li1, Jianping Wang2, Jingang Wu2, Jinhua Liu2, Weihai Bu2,

Waisum Wong2, Scott Yu2, Hanming Wu2, Shiuh-Wuu Lee2, Yangyuan Wang1

1 Institute of Microelectronics, Peking University, Beijing 100871, China (*emails: ruhuang@pku.edu.cn; r.wang@pku.edu.cn) 2 Semiconductor Manufacturing International Corporation (SMIC), Shanghai 201203, China

Abstract

The coupling effect between multi-traps in complex RTN is experimentally studied in scaled high-κ/metal-gate MOSFETs for the first time. By using extended STR method, the narrow “test window” of complex RTN is successfully expanded to full VG swing. Evident defect coupling can be observed in both RTN amplitude and time constants. Interesting nonmonotonic bias-dependence of defect coupling is found, which is due to two competitive mechanisms of Coulomb repulsion and channel percolation conduction. The decreased defect coupling is observed with increasing AC frequency. Based on the new observations on complex RTN, its impacts on the circuit stability are also evaluated, which show an underestimation of the transient performance if not considering defect coupling. The results are helpful for future robust circuit design against RTN.

Introduction As device dimensions continuously shrink, the random telegraph noise (RTN) plays as one of the major challenges in robust circuit design. Most previous work focused on single-trap induced RTN, which reveals the physical switching behavior of oxide defects [1-9]. Nevertheless, even in highly-scaled devices, there are still possibilities to have more than one trap in a device due to the wide distribution of trap number per device [4], and more traps will be activated due to circuit aging [10-11]. However, very few studies on the multi-trap induced RTN have been reported [12-13]. And how the defects are coupled together should be further examined. Moreover, in practical digital operations, the trap behavior needs to be characterized under AC bias, as has been studied by AC STR and AC RTN methods by our group [6-9], and AC TDDS method by Grasser et al. [1-2]. But the frequency dependence of the defect coupling in multi-trap induced complex RTN under AC condition has not been reported yet. In this paper, the coupling effects of multi-traps in complex RTN are experimentally studied in scaled high-κ/metal-gate MOSFETs for the first time. Challenges in characterizing coupled defects within different “test window” are addressed by extending DC/AC STR method. The bias and frequency dependences of defect coupling are extracted and discussed. And its impacts on circuit stability are also evaluated.

Devices and Characterization Method The devices used in this work are planar high-κ/metal-gate nFETs with ultra-thin SiO2/HfO2. Compared with single-trap induced simple RTN, characterizing complex RTN is challenging, since each trap has its own “detectable window” in conventional DC RTN measurement [1-3]. For one given trap, as shown in Fig. 1, RTN signal cannot be observed outside its “detectable window”, due to the huge deviation of capture and emission time at low/high VG. Unfortunately, the detectable windows of each trap do not have large overlap with varying VG in most cases, which makes the test window (for all traps) even narrower for characterizing complex RTN if using conventional DC RTN method measurement. To overcome this problem, the statistical trap response (STR) method [6,8] is adopted here to expand the narrow test window to full VG swing (GND-VDD). Fig.2 shows the schematics of DC/AC STR method. From recorded traces (Fig.3), the trap occupancy probability can be extracted, as shown in Fig.4 (DC) and Fig.5 (AC). By Eqs.1&2, the capture time constant can be obtained, as shown in Fig.6. The DC STR method can be verified by comparing with DC RTN results within its test window. Fig.7 shows the capture time constants extracted by STR and conventional DC RTN. The two methods have the same trend and close values. The AC STR can be verified by comparing with advanced AC RTN method proposed by us recently [7,9]. Fig. 8 shows the typical results of AC RTN, and Fig. 9 shows good agreement between both methods within their overlap region. Therefore, the narrow DC RTN test window can be accurately expanded to full VG swing by the proposed DC/AC STR method, as shown in Fig.10.

New Observations and Mechanism Analysis of Complex RTN

For complex RTN, we start from two-trap case. As shown in Fig.11, using conventional measurement, the complex RTN (with 4 levels induced by trap A and trap B) can be extracted only within the overlap of two individual trap windows. The coupling effect (the impact of trap B on trap A) can be obtained from extracting the trap A characteristics w/ or w/o trap B charged. The results show evident coupling on both RTN amplitude [Fig. 12(a)] and RTN time constants [Fig. 12(b)]. However, as expected, this complex RTN can be detected only in a narrow window (~50mV) using

IEDM13-77831.4.1978-1-4799-2306-9/13/$31.00 ©2013 IEEE

conventional measurement, which is not suitable for studies within full VG swing. Therefore, STR method is extended from single-trap case to multi-trap here, as shown in Fig.13. The occupancy probability of both trap A and B can be directly extracted, which provides much larger VG range than the conventional method (Fig.14). A valley in the occupancy probability can be clearly observed for both DC and AC conditions due to defect coupling effects, which deviates from the expected monotonic increasing trend in the single-trap case. This strong coupling region is interestingly found to be very close to the peak-Gm, which indicates that the defect coupling is correlated with current transport mechanism and will be discussed later. To further study the impact of defect coupling on RTN time constants, a new extraction method is proposed (Fig.15). As shown in Fig. 16, the normalized impacts of coupling are plotted with varying VG. Under DC condition, the defect coupling generally decreases with increasing VG. However, the nonmonotonic peak can be observed near peak-Gm, which is consistent with Fig.14. Under AC condition, the impact of defect coupling decreases with increasing AC frequency, yet the impact is still non-negligible especially at low VG (near VTH). The coupling effects between the two traps are fundamentally caused by the perturbation of the trap energy level (Et) and the local carrier density (within the capture cross section of the trap) induced by the other trapped charge. The shift of Et is most likely due to the Coulomb repulsion mechanism [14]. Take our result as an example, the occupation of trap B raises Et of trap A by Coulomb repulsion, thus decreases the occupancy probability of trap A. With the increase of VG, the Coulomb repulsion effect is weakened due to enhanced screening effect [14]. For the change of local carrier density, the blockade of one critical channel percolation path by other trap can be the possible mechanism, which will be discussed in detail below. Due to the impacts of random discrete dopants in the channel (and other effects such as metal-gate workfunction variations), the surface potential is fluctuated, which results in current percolation paths from source to drain [15]. Fig.17 is an example from atomistic TCAD simulations, which shows the evolution of channel percolation paths formation from low VG to high VG. At the VG near peak-Gm, the paths’ number is the largest, and then the paths begin to merge together and finally become a whole sheet of inversion channel. That is why that the coupling between trap A and B has a peak near peak-Gm in Fig.16. The measured ΔId amplitude in Fig. 18, which shows a nonmonotonic trend with VG, also confirms the formation of percolation paths in the channel [16]. As shown in Fig.19(a), at low VG, trap B has little impact on the percolation path passing through trap A, thus the local current density under trap A does not change. With VG increasing, more percolation paths are formed especially near peak-Gm , thus more than one paths could pass through trap A

[Fig.19(b)]. Therefore, trap B can block the newly-formed path and reduces the local current density under trap A, which results in capture time increase of trap A. But under high VG [Fig.19(c)], trap B can only reduce small amount of current due to the merging of percolation paths, and its impact on trap A is suppressed. Finally due to the enhanced screening effects combined with reduced percolation transport, the defect coupling is not obvious under very high VG. That is why the peak in the defect coupling due to the perturbation of local current density is located around peak-Gm. Therefore, in general, the defect coupling is modulated by the two competitive mechanisms of Coulomb repulsion and the channel percolation (indicated by Gm), as shown in Fig.20. Regarding the frequency dependence of defect coupling, Fig. 14 shows the reduced coupling between trap A and B with increasing f. Fig. 21 shows an extreme case, in which the slow trap H becomes inactive at higher f. When trap H is visible at DC or low f, it has impacts on the τc and the amplitude of the fast trap G; while when at higher f, there is no impacts of trap H on trap G. This can be understood in Fig. 22, where the effective occupation rate of slow trap H reduces fast (quickly below 1%) with increasing f, thus it is deactivated at high frequency.

Impacts of Complex RTN with Defect-Coupling on Circuit Stability

Based on the above new observations on complex RTN, its impacts on the stability of ring oscillators (RO) and SRAM cells are evaluated with defect coupling included. Fig.23 shows the period distributions of ROs, indicating reduced jitter if considering defect coupling. The read failure probability of SRAMs in Fig.24 also shows the reduced impacts of complex RTN if considering defect coupling. Therefore, there will be an underestimation of digital circuit transient performance if without including the defect coupling effect in complex RTN.

Summary The defect coupling in complex RTN in high-κ/metal-gate devices are experimentally studied under full bias swing with extended STR method. The nonmonotonic bias-dependence of defect coupling is observed for the first time, which is found due to two competitive mechanisms. The trap interaction is observed to reduce with increasing frequency. The impacts of complex RTN on RO and SRAM stability are also evaluated, which show performance underestimation if not considering defect coupling. The results are helpful for future robust circuit design against RTN. Acknowledgement: This work was partly supported by the 973 Projects (2011CBA00601), NSFC (61106085 and 60625403), and the National S&T Major Project (2009ZX02035-001). The authors would like to thank Prof. Tibor Grasser, Prof. Jiang Chen and Dr. H. Miki for the helpful discussions.

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Fig. 8. Typical results of AC RTN under various frequencies. The high level of the AC signal is 0.575V, while the low level is 0.45V. Under both levels, RTN can be observed. Vd is 0.05V for all the cases.

3.85

9

3.85

9

0 2 4 6 8

3.85

9

time (s)

1KHz

10 Hz

1 Hz

I d (μ

A)

Fig. 9. Comparison of τc extracted by AC RTN (obtained from RTN at 0.45V and 0.575V respectively) and AC STR method. Good agreement between the two methods within the overlap region can be observed.

10-1 101 103 105 107

102

103

104

AC STR @0.575V

frequency (Hz)

τ c (m

s)

period of AC signal

…0.575V

0.45V

…

…AC R

TN

Fig. 7. (a): Comparison of τc extracted from conventional DC RTN and DC STR method. (b): τc extracted from DC STR shows linear relationship with DC RTN. Considering their relationship, the small deviations of the two methods can be corrected by a shift of system error.

0.550 0.575 0.6001

10

100

10 20 30 40 50

20

40

60

80

Vd = 50 mV

(b)

τ c (m

s)

Vg (V)

DC RTN DC STR

Vg,set = 0.55V, 0.575V, 0.6V

(a)

τ c,D

C S

TR (m

s)

τc,DC RTN (ms)

Vd = 50 mV

Fig. 6. The frequency dependence of τc extracted from DC STR and AC STR method with Eq.1&2 under the gate biases of 0.55V,0.575V, 0.6V, respectively.

101 103 105 107

0.02

0.04

0.06

0.08 DC&AC STR

Vg,set=0.6V

Vg,set=0.575V

τ c (s

)

DCfrequency(Hz)

Vg,set=0.55V

Fig. 5. The trap occupancy probability p extracted from AC STR method under Vgset=0.55V, 0.575V, 0.6V, respectively. AC frequency is from 1 KHz to 1 MHz. The symbols are the experiment data while the lines are fitting results using Eq.2.

Fig.4. The trap occupancy probability p extracted from DC STR method under Vgset=0.55V, 0.575V, 0.6V, respectively. The symbols are the experiment data while the lines are fitting results using Eq.1.

30 60 90

0.2

0.4

0.6

0.8

1.0

15 30 45 60 10 20 30 40

p

Vg,set=0.575V

DC STR

Vg,set = 0.6VVg,set=0.55V

time (ms)

40 80 120 160

0.15

0.30

0.45

0.60

20 40 60 80 100 20 40 60 80

p

AC STR

Vg,set = 0.6VVg,set = 0.575VVg,set = 0.55V

time (ms)

1 KHz 10 KHz 100 KHz 1 MHz

Fig. 12. Extracted RTN amplitude (a) and time constants (b) of trap A w. & w/o. trap B charged. Evident coupling effects can be found in both RTN amplitude and time constants.

0.28 0.30 0.32

5

10

15

20

25

0.28 0.30 0.32

12

18

24

30

36

τe (s)

τ c (s

)

0

5

10

15

(b)

Vg (V)

Vg (V)

ΔId/

I d (%

)

Filled symbol: w/o trap B occupiedEmpty symbol: w/ trap B occupied

(a)

Fig. 10. The expanded DC RTN test window by the proposed STR method. DC RTN data is shown between the two bule lines.

0.0 0.2 0.4 0.6 0.810-4

10-2

100

102

time

cons

tant

s (s

)

Vg (V)

τc τe

detectable windowDC RTN

Fig.11. Characterization of the 4-level RTN (induce by trap A and B) using the conventional method. The complex RTN can be observed only within the overlap between two individual trap windows.

7.4

7.6

7.8

eg. Vg=1V

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eg. Vg=0.4V

two traps detectable outside the overlap of detectable windows of traps A, B

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I d (μ

A)

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trap B

(a)Vd

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50mV

tresetVgm

tset

Vg

Vgset

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Vg

(b)

treset

tset

Vgset

Vgm

References: [1] T. Grasser, et al., Microelec.Reliab., p.39, 2011; [2] T. Grasser, et al., IEDM, p.470, 2012; [3] H. Miki, et al., IEDM, p.450, 2012; [4] K. Takeuchi, et al., VLSI, p.53, 2009; [5] R. Huang, et al., Microelec. Reliab., p.1515, 2011; [6] C. Liu, et al., IEDM, p.571, 2011; [7] J. Zou, et al., VLSI, p.139, 2012; [8] C. Liu, et al., IEDM, p.466, 2012; [9] J. Zou, et al., VLSI, p.186, 2013; [10] B. Kaczer, et al., IRPS, p.26, 2010; [11] C. Zhao, et al., IEEE T-ED, p.1274, 2004; [12] E. Hsieh, et al., IEDM, p.454, 2012; [13] N. Tega, et al., IEDM, p.218, 2006; [14] M. Schulz, et al., APL, p.2649, 1993; [15] A. Asenov, et al., IEEE T-ED, p.839, 2003; [16] J. Franco, et al., IRPS, 5A.4.1, 2012.

Fig.2. Measurement schematics of DC STR method (a) and AC STR method (b). The oxide trap is trapping during tset and de-trapping during treset. The trap occupancy probability can be directly extracted from the recorded measurement traces.

Fig. 1. Characterization of DC RTN using conventional method within full bias swing. RTN can be observed only in the “detectable window” due to the huge deviation of capture and emission time or small RTN amplitude at low/high Vg. For the case of complex RTN, detectable windows of each trap do not have large overlap in most cases, resulting in a narrow test window.

0.0 0.2 0.4 0.6 0.8 1.0

10-1

101

103

time

cons

tant

s (s

)

τc τe

time (s)

Δ I d

(μA

) Vg=0.5V

DC RTN detectable window

ΔId ≈ 0 or τc>>τe ΔId ≈ 0 or τe>>τc

Vg0 VDD

I d (p

A) Vg=0V

time (s)

Δ I d

(pA

) Vg=1V

time (s)

narrow overlap of test window

trap 1

trap 2

Fig. 3. Typical results of measurement traces under Vg,set =0.6V (100 cycles) using the DC STR method. The step-like traces are caused by the random emission process of individual oxide trap.

0 200 400 600

2.3

2.4

2.5

I d (μ

A)

time (ms)

#1 #2 #3 #100

Vg,set = 0.6V DC STR

traces

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Fig.22. Frequency dependence of the extracted effective occupation rate of trap G and trap H. Trap H cannot be observed under higher frequency.

100 101 102 103

1

10

100

trap H unobservable

effe

ctiv

e oc

cupa

tion

rate

(%)

frequency (Hz)

0.575V 0.6V 0.625V

Fig. 23. Distributions of the periods in ring oscillator considering the impacts of complex RTN. Smaller variations can be found when considering coupling effects.

0.4 0.8 1.20.0

0.4

0.8

Volta

ge (V

)

time (ns)

1.17 1.20 1.23 1.260

150

300

450

coun

ts

period (ns)

w/ coupling effects

w/o coupling effects

5-stage RO

Fig. 24. Read failure probability of SRAM considering the impacts of complex RTN. About 28% overestimation can be found if not considering the coupling effects.

0.5 0.6 0.7 0.8

0%

20%

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d Fa

ilure

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e c eset

c e c ep 1 exp t

τ τ ττ τ τ τ

⎡ ⎤⎛ ⎞+= − −⎢ ⎥⎜ ⎟+ ⎢ ⎥⎝ ⎠⎣ ⎦

Eq.1 For DC STR extraction

Eq.3 Coulomb repulsion of two traps

( ){ }c 0 t f B1 exp E E k Tτ τ ⎡ ⎤= + −⎣ ⎦

( )12

inv gCoul m g FB

0

qt CqE 1 V V4 r 4kT WLπε ε

−⎡ ⎤

= + −⎢ ⎥⎣ ⎦

( ){ }'c 0 t f Coulm B1 exp E E E k Tτ τ ⎡ ⎤= + − +⎣ ⎦

eL cH eLset

cH eL cH eLp 1 exp t

2τ τ τ

τ τ τ τ⎡ ⎤⎛ ⎞+

= − −⎢ ⎥⎜ ⎟+ ⎢ ⎥⎝ ⎠⎣ ⎦

Eq.2 For AC STR extraction

Fig.20. The two competitive mechanisms, Coulomb repulsion effects (Eq.3) and local carrier density perturbation (could have the same trend of Gm ~ Vg) .

0.0 0.3 0.6 0.9

0

40

80

120

Vg (V)

E Cou

lm (m

eV)

0

10

20

30

Gm

(μS)

Competitive mechanisms

Defect coupling

Fig. 19. Atomistic simulation results of the current density considering the random dopant induced percolationmechanism (a) at low Vg, (b) at Vg near Gm peak point (c) at high Vg. The percolation mechanism can dominate when Vg near Gm peak point. One newly-formed percolation path passing through trap A could be blocked by trap B, which will reduce the local carrier density of trap A, thus increase the capture time.

Channel Direction

trap Atrap B

σr

Channel Direction

Low Vg(a)

Channel Direction

trap Atrap B

σr

Vg@Gm,max(b)

Channel Direction Channel Direction

trap Atrap B

σr

Channel Direction

High Vg(c)

Fig. 21. Complex RTN under DC and AC condition in Device#6, which includes two traps (trap G and trap H). The high level of AC signal is 0.6V.

3.6

3.6

3.6

3.6

DC RTN

AC RTN

AC RTN

AC RTNtrap H

trap G

1KHz

50Hz

1Hz

time (a.u.)

I d (μ

A)

Fig. 14. The extracted occupancy probability of trap A and trap B based on DC &AC STR methods. A valley can be found around the Gm peak point for both DC and AC conditions due to the defect coupling effects.

0.4 0.5 0.6 0.7 0.80.01

0.1

1

0.56 0.58 0.60

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0.4

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p

Vg (V)

trap A trap B

0.4 0.5 0.6 0.7 0.80.01

0.1

1

0.56 0.58 0.60

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0.40.6

AC STR

p

Vg (V)

trap A trap B

Fig. 15. Proposed extraction approach of time constant based on STR method. The four states are correlated to the observed current levels in Fig.13.

( )00 1 2 00 01 2 00 4 01

10 1 00 3 10 00 01 10 11

ci i

d dP k k P P k P k Pdt dtd P k P k P P P P P =1dt

1 / k i 1,2,3,4τ

= − + = −

= − + + +

= =

A B

A A

A

B

B

B

SiliconOxygen

k1

k3

(00)

(11)

(10) (01)

k2

k4

Fig. 13. Typical results of the measurement traces using STR method in case of complex RTN. Four levels can be seen ( AB : both traps are not charged, AB : only trap A is charged, AB : only trap B is charged, AB: both traps are charged).

0 30 60 90 120 150

0.8

1.0

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1.4

AB

AB

AB

I d

(μA

)

time (ms)

# 3 # 10 # 25 # 27 # 98

AB

traces

Fig.18. Total ΔΙd induced by trap A and B, which shows an abnormal nonmonotonic trend.

0.3 0.4 0.5 0.6 0.7

0.1

0.2

0.3

ΔI

d (μ

A)

Vg (V)

total amplitude of complex RTN

Fig. 17. Evolution of channel percolation paths formation from low Vg to high Vg. At the Vg near Gm peak point, the number of paths is largest, which indicates Gm value is positively correlated with the percolation paths.

900i

800 850750

700650 hgfed

600

c

10001100550

500ab k j

S D

ka

f

0.0 0.2 0.4 0.6 0.8

10

20

30

Gm

(μS)

Vgt (V)

Fig.16. The extracted Δτc/τc under DC (a) & AC STR (b) by methods proposed in Fig.15. Δτc= τc4 - τc1, which represents deviation of capture time (trap A) w/ or w/o the coupling effects of the other trap (trap B).

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0

3

6

9

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Vg (V)

Δτc/

τ c

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(b)

0.3 0.4 0.5 0.6 0.7

0.0

0.5

1.0

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DC STR

Δτc/

τ c

Vg (V)

(a)

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